Answer
The line through A and B is horizontal and has slope $m_{1}=0$.
Any perpendicular line to it has undefined slope.
Work Step by Step
$A=(x_{1},y_{1})=(2, \ 3)$
$B=(x_{2},y_{2})=(-1, \ 3)$
The increments in the coordinates are calculated as $\left\{\begin{array}{l}
\Delta x=x_{2}-x_{1}\\
\Delta y=y_{2}-y_{1}
\end{array}\right.$
$\left\{\begin{array}{l}
\Delta x=-1-2=-3\\
\\
\Delta y=3-3=0
\end{array}\right.$
The slope of the line that passes through A and B, if the line is nonvertical, ($\Delta x\neq 0)$ is calculated as
$m_{1}=\displaystyle \frac{\Delta y}{\Delta x}=\frac{0}{-3}=0$,
The line is horizontal.
Any line perpendicular to the line that passes through A and B is vertical, so its slope is undefined.
